Average Error: 17.6 → 0.0
Time: 1.2s
Precision: 64
\[\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y\]
↓
\[y \cdot \left(x - z\right)\]
\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y
↓
y \cdot \left(x - z\right)
double f(double x, double y, double z) {
        double r593356 = x;
        double r593357 = y;
        double r593358 = r593356 * r593357;
        double r593359 = z;
        double r593360 = r593357 * r593359;
        double r593361 = r593358 - r593360;
        double r593362 = r593357 * r593357;
        double r593363 = r593361 - r593362;
        double r593364 = r593363 + r593362;
        return r593364;
}
↓
double f(double x, double y, double z) {
        double r593365 = y;
        double r593366 = x;
        double r593367 = z;
        double r593368 = r593366 - r593367;
        double r593369 = r593365 * r593368;
        return r593369;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original17.6
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.6

    \[\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y\]

  2. Simplified0.0

    \[\leadsto \color{blue}{y \cdot \left(x - z\right)}\]

  3. Final simplification0.0

    \[\leadsto y \cdot \left(x - z\right)\]

Reproduce

herbie shell --seed 2020065 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (* (- x z) y)

  (+ (- (- (* x y) (* y z)) (* y y)) (* y y)))